Designer's Notebook: Positive Feedback

Most
of the time The Designer's Notebook is full of opinionated jottings about
creativity, storytelling, or the social effects of interactive entertainment
- in other words, blue sky. Every now and then, though, I feel compelled
to write something abstruse and technical about game design, something that's
more of a how-to than a why-to or a why-not-to. This is one of those times.
This month I'm going to talk about the effect that positive feedback has
on game balance.

What Is Positive
Feedback?

When we speak of feedback in everyday life, we're usually referring to that
horrible shriek that happens whenever the microphone in a public-address
system gets too close to the speakers. The mic picks up whatever's coming
out of the speakers and tries to amplify it again. More generally, feedback
occurs whenever the output of any system is "fed back" into it
as some kind of an input. What happens with the microphone and the amplifier
is an example of positive feedback - a situation that tends to amplify the
output of the system.
Positive feedback plays an important role in game design, although you don't
hear many designers talking about it. It can gravely harm a game if improperly
implemented, but it also has significant benefits. It's an element of game
design that every designer needs to understand and learn to use.

Before I go into how it works, though, let's look for a minute at the way
games are won and lost. When you happen across two friends playing a game,
what's the first thing you say? "Who's winning?" of course. That's
not always an easy question to answer. Some games have a metric that determines
who's ahead at any given time; others don't. In ping-pong, for example,
it's obvious: whoever has the most points is winning. In chess, it's less
clear because the victory condition - checkmating the king - is not defined
in terms of accumulating points. You can very generally say that whoever
has taken the most pieces is winning, but it's perfectly possible to win
at chess with fewer pieces than your opponent has.

In game design, positive feedback can be defined as occurring whenever one
useful achievement makes subsequent achievements easier. In other words,
whenever someone gains something in a game, it gets easier to make further
gains. If the role of positive feedback in a game is too great, then whoever
first obtains the slightest lead in the game is guaranteed to win, because
they just keep getting farther and farther ahead. This makes it sound as
if positive feedback is always undesirable, but it isn't; it's just a question
of employing it properly.

Positive feedback appears mostly in games in which the victory condition
is defined in numeric terms, and throughout the game you're working to achieve
that victory condition by accumulating something. In Monopoly, for example,
it's money. Obtaining money in Monopoly allows you to buy and improve properties,
which makes it possible to obtain more money. Positive feedback can also
appear in games in which a numeric advantage of some kind helps to achieve
a non-numeric victory condition. Although the victory condition in chess
is non-numeric, it does generally help to have more pieces than your opponent.

Balance Graphs
So what are some of the effects of positive feedback on games? I think it
will help to look at something I'm calling a balance graph, although there's
probably a different name for it in formal game theory. I've included several
of them below. A balance graph plots the progress of a zero-sum two-player
game. Time is represented on the horizontal axis. The vertical axis indicates
who's ahead by some numeric metric, usually the difference in points scored
by the two players. If player A is ahead, the number is above zero; if player
B is ahead, it's below zero. At the left edge of the graph, the beginning
of the game, the players are even at zero. Dotted lines at the top and the
bottom of the graph indicate the victory condition for either player A or
B.

My first balance graph represents a simple sprint foot race in which player
A is a faster runner than player B. A immediately goes ahead and remains
ahead for the duration of the race. Straightforward races have no positive
feedback. Gaining the lead does not make it easier to retain or increase
the lead. (In fact, there's psychological evidence to suggest that the opposite
is true: runners try harder if there's someone slightly ahead of them. When
Roger Bannister was training to break the four-minute mile, he ran with
pacesetters who ran in front of him. This phenomenon has also been observed
in racehorses and sled dogs. However, it isn't part of the rules of the
game, which is what we're concerned with here.)

Figure 1

The next graph is an example of an unbalanced, i.e. unfair, game - whether
or not it includes positive feedback. Assuming that A and B are of equal
skill and there is no element of chance involved, something about the rules
is giving A an advantage, such that she takes the lead and maintains it
throughout a very short game.

Figure 2

In Figure 3 we have a stalemate, a game that goes on forever with neither
player able to assume a commanding lead. This is a game that's too balanced:
neither player is able to achieve victory. The children's card game War
is a good example of this kind of game: it's all luck, no skill, and no
positive feedback, so it can go on for hours. This illustrates why positive
feedback is a useful thing: it helps to prevent stalemates. Once a player
assumes enough of a lead, the advantage that positive feedback confers guarantees
that he will win.

Figure 3

Figure 4 illustrates a game that's balanced, but positive feedback sets
in too soon, producing a fair but very short game. B gains a slight advantage,
then A retakes a slight lead, then B again, then A takes a longer lead and
promptly wins the game.

Figure 4

The ideal game, in my opinion, starts off even and balanced, but slowly
becomes unbalanced over time until one player inevitably wins - preferably
the better player! Figure 5 shows one example, although in this case player
B struggles on valiantly for quite a while.

Figure 5

Once a player's lead becomes commanding, the game shouldn't take too long
to finish. This is one of the (very few) problems with Monopoly. From the
time that it becomes clear that one player must win until he has actually
bankrupted all the other players is usually half an hour or more. The other
players just have to sit and wait through their slow slide into oblivion.

Positive Feedback in Games
So let's look at some examples of games with and without positive feedback.
As I mentioned before, races and most other athletic competitions don't
have positive feedback - at least, not designed into the rules. Scoring
points in basketball doesn't make it any easier to score further points.
Nor do most card games: cribbage or rummy, for example. On the other hand,
war games definitely do have positive feedback, especially if the victory
condition is simply to wipe out all the other player's units. Destroying
an enemy unit confers an advantage to the player who does it. The unit no
longer there to fight back, so it's easier to destroy the next unit, and
so on.

Another genre of computer game that has positive feedback is single-player
role-playing games. You start off with poor weapons; you kill some monsters;
you get some treasure, and you use it to buy better weapons. The better
weapons enable you to kill more monsters, you get more treasure, you buy
still better weapons, and so on.

Positive feedback needn't have a direct influence on the path to victory;
it can appear in other areas of a game as well. While I was at Bullfrog
Productions, I was lead designer on a new game (never published, alas) called
Genesis: The Hand of God. Genesis was a god game in the spirit of Bullfrog's
original Populous, in which you could affect the weather of a landscape
with divine power, drawing on mana generated by your simulated worshippers
to do so. One of our innovations was that there were several different types
of mana, depending on the nature of the landscape in which your worshippers
lived. For example, if they lived in a wet area, you got a lot of water
mana, which you could use to make rain. Of course we realized immediately
that this was a positive feedback loop: the more water you had, the more
water you could get. On the other hand if your people lived in a desert,
it was very difficult to make rain because they were producing very little
water mana.

In the end we concluded that this wasn't a problem for the game. Making
rain in a wet area made it wetter, but so what? If you made it rain all
the time you would drown your own people, and there was no benefit in that.
We also thought that making the desert bloom shouldn't be too easy at first,
but once you got it started, it should get easier. Although it was positive
feedback, it didn't endanger the balance of the game because it didn't confer
a direct advantage over your opponents.